KRASNAYA POLYANA, Russia — A couple years ago, they made a rules change in the giant slalom. Citing the interest of athlete safety, they made the skiers change to longer, straighter skis.

Those skis are way harder to turn. Ted Ligety, the American who had ruled the giant slalom, complained bitterly.

And then he figured out a way to ski on those new skis, lower and longer in the turns, that further separated himself from everyone else in the world. He could now win races by astonishing margins.

At Wednesday’s men’s super-G at Rosa Khutor, Ligety put on a clinic to win the first American Alpine skiing gold of these Olympics. Indeed, he won big. It was one of the great moments of the 2014 Games. Here, for the entire world to bear witness, was sheer excellence — the excellence the sport demands as well as the excellence the man demands of himself.

It also marked a profound moment in U.S. ski history — past, present and future.

Bode Miller announced after the race that his knees are bothering him and he is done at these Olympics; he will not ski Saturday’s slalom. He said, however, he intends to finish out the season. Miller is 36. There can be no question that — whatever Miller’s future — Ligety, 29, is now positioned to be The Man on the U.S. Ski Team.

“He carries so much speed and just doesn’t really make mistakes. Those are the things that separate him,” Miller said when asked to describe Ligety’s GS skiing.

“Other guys carry speed for a couple turns. They struggle a little bit. He just carries it smooth, top to bottom. He consistently puts time on guys the whole way down. He’s not doing a miracle in one section. He just pulls time on top, pulls more time in the middle, pulls more time on the bottom. There’s no question who is the best GS skier right now.”

Ligety now has two Olympic gold medals. His first came in the combined in Torino in 2006. He and Andrea Mead Lawrence, who won the slalom and the GS in Oslo in 1952, are now the only two American skiers with two Olympic gold medals in Alpine.

Ligety is the first man in Olympic history — no matter the country — to have won gold in giant slalom and the combined. Not Hermann Maier, Toni Sailer, Jean-Claude Killy, Kjetil Andre Aamodt, Lasse Kjus, or anyone else you might name.

You can bet this first Olympic GS gold for an American male skier is a big deal for the U.S. Ski Team program — there are potential donors and board members who flew all the way here through this weekend, ignoring all the controversies, just to see Ligety and 18-year-old sensation Mikaela Shiffrin. Ligety held up his end of the deal. Shiffrin, the world slalom champ, finished fifth Tuesday in the women’s GS, not her best event. She goes Friday in the slalom.

If development doesn’t seem all that sexy, consider this: Ligety and a few others on the U.S. team have trained here, on this very hill, a total of two weeks over the past two years. One particular turn on the second run gave a number of the racers fits. The first time Ligety trained here, he took five runs. And, as he said, “I didn’t finish a single one of my five runs because I was trying to take all the speed off that. So I knew how big a jump that was and how critical that was to the course.“

The medal Wednesday also means the U.S. Alpine team has won four medals in Sochi. One more ties for the second-best performance ever (the 1984 team). The 2010 team won eight — far and away best-ever.

Another slice of history: it was precisely 30 years ago — Feb. 19, 1984 — that Phil Mahre won gold in the slalom in Sarajevo, brother Steve taking silver.

Because of the 2006 gold, it wasn’t so much that Ligety came to Sochi with the burden of having to prove himself at an Olympics. Moreover, he has ruled giant slalom for seven seasons. Beyond which, at last year’s World Championships, he won three golds — in the GS, super-G and super-combined, the first man to win three world golds since Killy in 1968.

The expectation here, though, was simple: in the United States, people tend to pay attention to Alpine skiing in a big way once every four years.

Welcome back to the Olympics, Mr. Ligety.

“In some kind of way,” said Bill Marolt, the president and chief executive of the U.S. Ski and Snowboard Association, Ligety “needed this gold medal here to confirm all that he has done.”

“It creates a lot of pressure, but on the other hand it creates a lot of opportunity. The thing neat about Ted,” Marolt said, “is that he has this unbelievable ability to focus and, in the moment, grab the whole prize. He just represents all that we believe in — get in unbelievable shape physically, work like hell and stay in the moment. It was awesome to be part of.”

Earlier at these Games, Ligety had a shot at a medal in the super-combined but uncharacteristically did not ski aggressively; he finished 12th. A few days later in the super-G, he took 14th.

“The combined was definitely a huge disappointment, mostly because I knew I could have skied a lot faster,” Ligety said, adding that in the super-G he skied “great” but simply made a mistake. “That’s frustrating but at least I knew I was skiing fast. I’ve known coming in here my GS was in a good spot. I’m happy to be able to ski the way I know how to ski.”

The women’s giant slalom Monday was messy — rain, snow, sleet, fog. Conditions Wednesday morning were perfect — bright, blue skies with the snow icy, just the way racers like it. It was exactly 32 degrees at race time, the snow exactly 32, too.

Ligety further had the decided advantage of going No. 7 Tuesday morning in Run 1, after his main rivals, France’s Alexis Pinturault and Austria’s Marcel Hirscher.

Pinturault went No. 1, finishing in 1:22.4; Hirscher No. 3, 1:22.47.

Ligety then put down a run of incredible aesthetic and athletic grace and power. A slow-motion camera would show his body perfectly in alignment with the mountain as he weaved through the gates.

The plan, he said, was to “really just nail a couple of the big rolls,” and be intelligent everywhere else in assessing risk.

“The hill,” he would say later, “is not so difficult skiing-wise. It’s difficult tactically. I was trying to be smart over those big tactical terrain changes and then push as hard as I could in the sections where I could take some risk and I knew I could push hard.”

He was 1.33 seconds ahead of the field. There were, literally, gasps and oohs and ahhs from seasoned watchers in the press room. In ski racing, 1.33 seconds might as well be a year.

By the time the field wound through the top 30, only Ondrej Bank of the Czech Republic was even within shouting distance— the sound of Bank’s skis telling the story of his slash-and-dash down the course from the No. 28 hole to within 93-hundredths of a second. Bank’s best-ever World Cup finish: a giant-slalom fifth in December, 2010.

Germany’s Stefan Luitz actually had gotten to within 59-hundredths of a second but then straddled the final gate with his right ski. He was DQ’d. “Maybe,” Luitz said, “I let my head go.”

How good was Ligety in Run 1? He led every one of the four splits. Once more — that lead was 93-hundredths. As an exercise in math, 93-hundredths covered every guy in the field from third through 21st — Simoncelli, 1.27 behind, through American Tim Jitloff, 2.15 back.

Hirscher, leading the current World Cup GS standings, finished Run 1 in seventh, 1.39 behind. Pinturault, second in the season standings, ended Run 1 in sixth, 1.36 back.

Miller was never a factor. He finished Run 1 2.56 behind, Run 2.53, in 20th. He said his left knee in particular wasn’t feeling quite right; his precise word was “jankied.” Also, he and his tech team, after watching the women’s GS Tuesday, figured on soft snow, and then came out Wednesday to find conditions were instead excellent. After the first run, he said, “I knew after four turns, Jesus, I’m in trouble.”

Ligety, meanwhile, said between runs he no longer had “to take the mega-risk,” adding, “It’s really important to still go as hard in the sections you can so you’re making up time in the normal turns and just be smart to carry speed through those really difficult tactical sections.”

He also said, for emphasis, “You can’t let up in ski racing. Ski racing is the kind of thing where you can blow leads really quickly. And nothing is truly safe.”

He did not let up. He almost got caught on a right-footed turn about a third of the way down Run 2 but saved himself from what would have been a catastrophic fall and, again, because he knew the hill, ran hard but intelligently, giving back time with only the 14th-fastest in Run 2.

Hirscher would finish fourth, just out of the medals; Pinturault would get third. Another French skier, Steve Missillier, would get second.

The final difference Wednesday between first and second? A whopping 48-hundredths of a second. The slo-mo cameras, again, were so revealing — Ligety’s skis, in a beautiful physics experiment, gliding along at a 90-degree angle to the slopes.

“Today,” Ligety said, “was awesome. There’s really no other way to put it.”